Ask the master of mathematics to explain the ratio of Yin and Yang in each of the 24 solar terms in this Taiji diagram, such as the ratio of the area of Yin to the area of Yang between the solar terms

Ask the master of mathematics to explain the ratio of Yin and Yang in each of the 24 solar terms in this Taiji diagram, such as the ratio of the area of Yin to the area of Yang between the solar terms from summer to summer. In fact, this problem is not difficult, but it is too much trouble. If you have to do the same thing 24 times, why bother? Make one.

Let the circle radius of Taiji diagram be 6 and the angle unit be radian. In terms of symmetry, we only need to study the summer solstice-the autumnal equinox-the winter solstice.

It is easy to find out that the Taiji curve can be expressed as ρ=﹙6/π﹚×﹙θ+π/2﹚[ for example, θ = π/6 ﹚ = 4] in polar coordinates.

Let's calculate the area ratio of Yin and Yang in Qi Festival from summer to Millennium. Total area = π× 6? /24=3π/2

Poplar area = ∫ [π/ 12, π/6]- 1/2-ρ? dθ=6θ？ /π? -9θ? [π/ 12, π/6] = 9π/32 /π+9θ/2.

Yin area = 3 π/2-9 π/32 = 39 π/32 Yang area/Yin area = 9/39.